Question

A car is moving on a circular path of radius 500 m with speed of 30 ms^-1. If at any instant the speed of the car increases at the rate of 2 ms^-1, then find the resultant acceleration of the car:

(a) 4.7 ms^-2

(b) 3.8 ms^-2

(c) 3 ms^-2

(d) 2.7 ms^-2

Answer 1

Correct option is : (d) 2.7 ms^-2

Centripetal acceleration,

\(a_c = \frac{v^2}{r} = \frac{(30)^2}{500} = 1.8\ ms^{-2}\)

Tangential acceleration, a_T = 2 ms^-2

∴ Resultant acceleration

\(a = \sqrt{a_c^{2} + a_T^{2}} = \sqrt{(1.8)^2 + (2)^2}\)

r a = 2.7 ms^-2

Thus, option (d) is correct.